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I

~

i I I i 1 i

OWL, TM-2029

Contract No. W-7405-eng-26

General Engineering Division

INVESTIGATION OF ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM MUSING A MOLTEN-SALT BREEDER REACTOR

W. K. Crowley J. R. Rose

NOVEMBER 1967

OAK RIDGE NATIONAL LABORATORY

UNION CARBIDE CORPORATION for the

U. S. ATOMIC ENERGY COMMISSION

”

3 . c

iii

CONTENTS

Page

A b s t r a c t . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1. INTRODUCTION. 0 0 . . 1 2. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . 4 3. DEVELOPMENT OF ANALYTICAL METHODS . . . . . . . . . . . . . 6

Steady-State Condition . . . . . . . . . . . . . . . . . . . 7

Derivat ion of Equations . . . . . . . . . . . . . . . . . 8

Calcula t iona l Procedure . . . . . . . . . . . . . . . . . 15

Trans ien t Case . . . . . . . . . . . . . . . . . . . . . . . . 17

4. PARAMETRIC STUDIES . . . . . . . . . . . . . . . . . . . . Cases Studied for Steady-State Condition . . . . . . . . .

5 . CONCLUSIONS . . . . . . . . . . . . . . . . . . . . . . . Appendix A. EQUATIONS NECESSARY TO CONSIDER A MULTIENERGETIC

G A M M A C U R R E N T e . * o . o o . . o . . . . . . . .

Appendix B. EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT . . . . . . . . . . . . . . . . . . .

Appendix C. VALUES OF PHYSICAL CONSTANTS USED I N THIS STUDY . Appendix D. TSS COMPUTER PROGRAM . . . . . . . . . . . . . .

Case Studied f o r Transient Condition . . . . . .

Appendix E. NOMENCLATURE . . . . . . . . . . . . . . . . . .

. 20

0 20 . 29

35

. 41

. 44

. 46

. 47

. 60

I

? 3

'c c:

V

LIST OF TABLES.

Table Number

1

2

3

4

5

6

7

D. 1

D.2

D. 3

Title - Results of Investigation of First Steady-State Case

Results of Investigation of Second Steady-State Case

Results of Investigation of Third Steady-State Case

Results of Investigation of Fourth Steady-State Case

Results of Investigation of Fifth Steady-State Case

Results of Investigation of Sixth Steady-State Case

Results of Investigation of Seventh Steady-State Case

Computer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generation

Range of Parameters of Interest in Studies Made of Proposed Wall With An Incident Gamma Current of 1 x lola photons/cn? *sec

Typical Data for 32 Cases With One Energy Group for the TSS Computer Program

TSS Output Data at the Bottom of the Air Channel for One Case

TSS Output Data at Top of the Air Channel for One Case

Page Number

22

23

24

25

26

27

28

31

36

54

58

59

$ 2

e W

vii

LIST OF FIGURES

Figure Number

1

2

3

4

5

D. 1

Title

Proposed Configuration of Reactor Room Wall

Proposed Configuration of Reactor Room Wall With Corresponding Terminology

Designations Given Segments of Reactor Room Wall for Study of Transient Conditions

Temperature Distribution ' in Proposed Reactor Room Wall With Internal Heat Generation Rate Maintained During Loss-of-Wall-Coolant Transient Period

Temperature Distribution in Proposed Reactor Room Wall With No Internal Heat Generation During the Loss-of-Wall-Coolant Transient Period

Assembly of Data Cards for TSS Computer Program

Page Number

2

6

18

33

34

53

7 f

z INVESTIGATION OF ‘ONE CONCEPT OF A THERMAL SHIELD FOR THE ROOM HOUSING A MOLTEN-SALT BREEDER REACTOR

‘ : Abstract’:’ !C. 3

The concrete providing the biological shield for a 250~Mw(e) molten-salt breeder reactor must be protected from the gamma current within the reactor room. A con- figuration of a laminated shielding wall proposed for the reactor room was studied to determine (1) its abil- ity to maintain the bulk temperature of the concrete and the maximum temperature differential at levels be- low the allowable maximums, (2) whether or not the con- duction loss from the reactor room will be kept below a given maximum value, (3) whether air is an acceptable medium for cooling the wall, and (4) the length of time that a loss of this coolant air flow can be sustained before the bulk temperature of the concrete exceeds the maximum allowable temperature. Equations were developed to study the heat transfer and shielding properties of the proposed reactor room wall for various combinations of lamination thicknesses. The proposed configuration is acceptable for (1) an incident monoenergetic (1 Mev) gamma current of 1~ x 1012 photons/c& l see and (2) an insulation thickness of 5 in. or more. The best results are obtained when most of the gamma-shield steel is placed on the reactor side of the cooling channel.

1. INTRODUCTION

t

Thermal-energy molten-salt breeder-reactors (MSBR) are being studied

to assess their economic and nuclear performance and to identify important

design problems. One design problem,identified during the study made of

a conceptual 10001Mw(e) MSBR power plant1 was that there will be a rather / . intense gamma current in the-room in-which the molten-salt breeder reactor

is housed. The concrete wall.providing the biological shield around the

reactor room must be protected fromthis intense gamma current to limit

: ‘P. R. Kasten, E. Si Bettis, and R. C. Robertson, “Design Studies of

lOOO-Mw(e) Molten-Salt Breeder Reactors, Ridge National Laboratory, August 1966.

” USAEC Report ORNL-3996, Oak

2

gamma hea t ing i n the concrete.

from the high ambient temperature i n the reactor room.

method o f p ro tec t ing the concrete is the app l i ca t ion of l aye r s o f gamma

and thermal sh ie ld ing and in su la t ing materials on the r eac to r s i d e of the

concrete.

r eac to r room i s i l l u s t r a t e d i n Fig. 1.

Further, the concrete must be pro tec ted

One poss ib l e

A proposed configurat ion of the layered-type wal l f o r t he

ORNL OW# 61-12000

SKIN7 INSULATlON 7 r STEEL 7 rCONCRElE

AIR

Fig. 1. Proposed Configuration of Reactor Room Wall.

The study reported here was made t o i nves t iga t e t h i s proposed con-

f igu ra t ion of a r e a c t o r room w a l l for the modular concept? of a 1000-Mw(e)

MSBR power p l an t . This modular p l a n t would have four separa te and i d e n t i -

cal 250-Mw(e) r eac to r s with t h e i r separa te s a l t c i r c u i t s and heat-exchange

loops.

no t the proposed configurat ion fo r the reactor room wal l w i l l

1.

This prel iminary invest igat’ ioa was made to determine whether o r

maintain the bulk temperature o f t he concrete por t ion o f t he w a l l at

l e v e l s below 212’F,

maintain the temperature d i f f e r e n t i a l i n the concrete lamination a t

l e s s than 40°F (a f a i r l y conservat ive value), and

2.

3, maintain the conduction loss from a r eac to r room a t 1 Mw or less. This study w a s a l s o performed t o determine whether o r not a i r i s a s u i t -

ab l e medium f o r cool ing the reactor room wall and t o determine the length

o f t i m e over which the l o s s o f t h i s a i r flow can be t o l e r a t e d before the

3

i 2 3

bulk temperature of the concrete lamination. exceeds the maximum allowable temperature of 212'F.

u b w

Analysis of the proposed configuration for the wall of the reactor room was based on an investigation of the heat transfer and shielding properties of t osite wall sho n Fig. 1. Equations were devel- oped that would these properties to be examined parametrically for various combinations of lamination materials and thicknesses

L r

c

4

2. SUMMARY

\ Methods were devised to parametrically analyze a comp

with internal heat generation produced by the attenuation current from the reactor room. were considered. Thirty-one equations gram was written to examine the heat transfer and shielding properties of the proposed wall for various combinations of lamination materials and thicknesses. photons/ca? sec through 3 x 10” photons/ca? *sec were examined. difference approach, with the differencing with respect to time, was

Both steady state and tran

Incident monoenergetic (1 MeV) gamma currents of 1 x le2 A finite

used in the transient-condition analysis to obtain a first approximation of the amount of time that the proposed wall could sustain a loss of coolant air flow.

The results of these studies indicate that the proposed configuration of the laminated wall in the reactor room is acceptable for the cases considered with an incident monoenergetic (1 MeV) gamma current of 1 x 1Ol2

photons/ca?*sec and a firebrick insulation lamination of 5 in. or more. Under these conditions, a total of approximately 4 in. of steel is suffi- cient for gamma shielding. The best results are obtained when the thick- nesses of the mild-steel gamma shields are arranged so that the major portion of the steel is on the reactor side of the air channel. the proposed configuration of the laminated wall for the reactor room does not protect the concrete from excessive temperature when the incident monoenergetic gamma current is 2 x lola photons/ca? osec.

However,

With an incident monoenergetic (1 MeV) gamma current of 1 x 10’” photons/c$ sec, the proposed laminated wall will maintain the temperature differential in the steel to within 10°F or less for all the cases studied. The differential between the temperature of the steel-concrete interface and the maximum temperature of the concrete is less than 1S0F for all the cases studied. The values of both of these temperature differentials are well below a critical value.

Based on the assumption that the floor and ceiling of the reactor

room have the same laminated configuration as the walls, the proposed

I ? 2

w s

w L

5

wall will allow the conduction loss from the reactor room to be maintained

at a level below 1 Mw for an incident monoenergetic (1 Mev) gamma current

of 1 x 10la photons/ct#*sec if the thickness of the firebrick insulation

lamination is 5 in. or more and if at least 4 in. of mild-steel gamma

shielding is ikiuded. _ With a coolant air channel’width of 3 in. and an air velocity of

50 ft/sec, air is an acceptable medium for cooling the.proposed reactor

room wall. If the ambient temperature of the reactor room remains at

approximately 1106OF and if the. gamma’current is maintained at 1 x lOla

photons/& 9 set, the temperature of the concrete will remain below the

critical level.(212oF)‘for approximately one hour after a loss of the

coolant air flow. If a zero incident gamma’current is assumed,.the

nperu&ssibleii loss-of-coolant-airiflow time is greater than one hour but

less than two hours.

To determine whether-or not a conduction loss of 1 Mw will permit

maintenance of the desired ambient temperature within the reactor room

without the addition of auxiliary cooling or heating systems, an overall

4 energy balance should be performed when sufficient information becomes

available. This balance should start with the fissioning process

reactor and extend-out through the wall of the reactor room to an

available. This balance should start with the fissioning process

reactor and extend-out through the wall of the reactor room to an

surface.

in the

outside

6

3. DEVELOPMENT OF ANALYTLCAL METHODS

I n the modular concept o f a 1000-Mw(e) MSBR power plant,' t he four

i d e n t i c a l but separa te 250-Mw(e) molten-salt breeder r eac to r s would be

housed i n four separa te r e a c t o r rooms.

sa l t hea t exchanger and one blanke

would a l s o be housed i n each r eac to r room along with the reactor.

items of equipment are to be located 11 f t from each o t h e r in the 52-f

long r eac to r room t h a t i s 22 f t wide and 4 8 - f t high.

primary fue l - sa l t - to -coolant -sa l t hea t exchanger are respons

gamma cu r ren t i n each o f the r eac to r rooms.

One primary fuel-sal t - to-coolant-

a l t - to -coolant -sa l t hea t exchanger

These

The reac to r and t h e

The proposed configurat ion

t i o n s devised t o p r o t e c t the concrete from the gamma cu r ren t

r room is shown i n Fig. 2 with the corresponding terminology used i n the parametric s t u d i e s made o f the omposite w a l l .

'P. R. Kasten, E. S. Bettis, and R. C. Robertson, "Design Studies o f lOOO-Mw(e) Molten-Salt Breeder Reactors," USAEC Rep0 Ridge National.Laboratory, August 1966.

ORNL- 3996, Oak

ORNL Dug. 67-10001

I AIR

Fig. 2. Proposed Configuration o f Reactor Room Wall With Corres- ponding Terminology.

- 4

U *

2 7

lj ‘i In the direction from the interior of the reactor room out to the

outer surface of the wall (left to right in Fig. 2), the layers of mate-

rial comprising the wall,are a-stainless steel skin, firebrick insulation,

a mild-steel gamma shield, an air channel, a mild-steel-gamma shield, and

the concrete;biological shfeld: The thicknesses of the firebrick insula-

tion and each of, the two,mild-steel gamma shields are considered to be

the-variable parametersin this study. The thickness of the stainless

steel skin is fixed at l/16 in., the thickness of the concrete is either

8. ft for an exterior wa.ll:or 3 ft for an interior wal.1, and the width of

the air channel is fixed at.3 in.

The temperature of the interior surface of the reactor room wall is

-considered to be uniform over ‘the surface and constant at 1100’F. The

temperature of the exterior surface of the wall is -considered to be uni-

form over the surface and constant at SOoF for the 8-ft thickness of

concrete (the temperature of the earth for an exterior wall) or at 70°F

c for the 3-ft thickness of concrete (the ambient temperature of an adjoin- c ing room within the facility for’an interior wall). The temperature of

ci the coolant air is assumed to be lOOoF at the bottom (entrance) of the

air channel, and the velocity of the air is assumed to’be SO ft/sec.

The situation examined is>basically one involving a composite plane

wall with internal heat generation caused by the attenuation of the gamma

current. from the reactor room. Two conditions were considered: the

steady-state condition and the transient condition. The steady-state

condition was considered first and the transient condition was considered . later when the problem of a loss of wall coolant was examined.

,’ 1

Steady-State Condition :

Equat,ionk- were develoPed .to mallow the heat transfer and shielding

properties of the--composite- wall, shown in Fig. 2, to be examined para-

metrically for various combinations of lamination materials and thick-

i nesses. A one-dimensional analysis was used, assuming that the tempera-

LJ tures of the interior and exterior surfaces of the wall were constant and

E uniform. \

8

Derivation of Equations

A s teady-s ta te energy balance on a d i f f e r e n t i a l element o f the r eac to r

room wall can be expressed semantical ly as follows. The hea t conducted

i n t o the element through the l e f t face during the time A0 p l u s the hea t

generated by sources i n the element during the t i m e A0 equals t h e - h e a t

conducted out of the element through the r i g h t face during the time 08.

This i s expressed a lgeb ra i ca l ly i n Eq. 1.

where

k = thermal conductivity, Btu/hr*ft*'F,

A,. = u n i t a r ea on wall , f t a , 0 T = temperature, F,

x = dis tance perpendicular t o sur face o f the w a l l , f t , 0 = time, hours, and

Q = volumetric gamma hea t ing rate, Btu/hr*ft?.

Application of t he mean-value theorem t o dT/dx g ives t h e expression o f

Eq. 2.

where M i s a po in t between x and x + Ax. Eq. 1 and A0 i s canceled.

Equation 2 i s s u b s t i t u t e d i n t o

The common term -& - ::Ix i s canceled, and i t i s noted t h a t

' = @T/d$. The r e s u l t i n g expression i s given i n Eq. 4. Q 4 & = - k p , g l & . rtaT

M Dividing Eq. 4 by &Ax and a l lowing& to approach zero as a l i m i t so

t h a t a value a t M becomes a va lue a t x, the volumetric gamma hea t ing r a t e ,

CPT Q = - k q ,

L - u c ¶

9

A

Equation 5 is integrated twice, and if Q # Q(x),

T(x) = 3 x? + G x + C, . ( 6 )

The applicable boundary conditions for any particular lamination in the wall are T = ‘I& at x = 0 and T = T L of the lamination interface at zero location designated in Fig. 2 and L = the thickness of the material in a lamination in feet. Tkese con- ditions are applied to Eq. 6.

at x = L, where T, = the temperature

i

The internal heat generation encountered in this study is caused by a deposition of energy in the form of heat when the gamma rays are atten- uated by the materials in the wall of the room. uation of the gamma rays, the volumetric gamma heating rate, Q, is a function of the distance perpendicular to the surface of the wall, x. The equations derived in this study are based on the assumption that the incident gamma current is monoenergetic, but appropriate equations for a multi-energetic gamma current are given in Appendix A. For a mono- energetic g a m a current where buildup and exponential attenuation are considered, the equation for Q(x) becomes

Because of this atten-

Q(x) = Q[Aewx + (1 - A)e -PPX],-Px , where

A, (31, and p = dimensionless constants used in the Taylor buildup

enuation coefficient, ft-1. When

= the volumetric te at the surface on the reactor

n, Btu/hr*ft?, current, MeV,

go = incident gamma current, photons/cn? sec, and % = gamma energy attenuation coefficient, ft-1.

10

Substituting Eq. 9 into Eq. 5,

Equation 10' is integrated twice to yield -

+ c ; x + c q = o . (11) The previously stated boundary conditions are still applicable, and the result of applying these conditions to Eq. 11 is that

The temperature distribution in any particular lamination of the wall is given by Eq. 12 when the appropriate constants for that lamination are used. Equation 12 is used primarily to determine the maximum temperature in the concrete and to determine the location of this maximum temperature. To locate the position of the maximum temperature in the concrete, Eq. 12 is differentiated with respect to x, the resulting derivative (dT/dx) is set equal to zero, and the equation is solved for X. The value of x

obtained gives the distance from the concrete-steel interface to the position of the maximum temperature in the concrete.

Equation 13 is a transcendental equation in x, and as such, it must be solved by using a trial-and-error technique. in Eq. 13 that contain x, and these terns are rearranged to put Eq. 13 in a form more easily solved by trial and error.

There are only two terms

= $6 - TL> + + k (YC A

i pL(c%- 1)

(a - l)= l - e I

+ (B1+-lfa 1 1 - e -cl.L(cr - 1) . (14)

All of the coefficients on the left side of Eq. 14 are known, and all of

the terms on the right side are known. Therefore, Eq. 14 may be written

in the form

%e -a,x; ke =%kx = k ,; (15)

where the K’s and a’s are calculable numbers. When Eq. 14 is solved for

x, this value of x is called xT.max; The va1ue.x = xT max is substituted

into Eq. 12 to obtain the maximum temperature of the concrete.

To determine the magnitude of the conduction loss, q*, from the

reactor room, equations were written to give the temperature drops across

each separate lamination in the~wall. These equations are simple con-

duction and convection equations in which all of the heat generated in a

particular Lamaination is assumed to be conducted through a length equal . to two-thirds of the thickness of the particular lamination. The total

amount of gamma heat, q TI deposited per unit area in a direction normal to

the face of the wall is found for any particular lamination by integrating

Eq. 9 over the length, L, of the particular lamination.

qT = J

L & [Aepta - ‘) +-. (1 - A)e”~x(p + ‘)] dx . (16) ._~~~

)

=Sro2 -

.-. -

A 1)(

eCrL(a - 1) _ .---:ll - ++ e 1

-PUB + 0 -113 ’ (17) _-

where Q is the incident volumetric gamma heating rate.

There are two possible ways to evaluate the incident volumetric

gamma heating rate at some.particular material interface, which shall be

referred. to as the “j-th” interface.~ The first. way is ~to calculate the

gamma current, @ o(J)’

at each’interface. To obtain Q W’

this calculated

L value of ip is substituted into the equation 1 o(j)

‘(3 = E@o(j)% l

12

The second method o f eva lua t ing the inc ident volumetric gamma heat ing

rate involves subt rac t ing t h e t o t a l amount of gamma hea t deposi ted p e r

u n i t area i n t h e j - t h lamination, q .I u n i t area inc ident upon the j - t h lamination

gamma energy cur ren t p e r u n i t area inc ident upon the face of t he follow-

from the gamma energy cu r ren t pe r

to approximate the qo(j),

ing lamination qo(j + 1) *

“(j + 1) = qo(j) - q j -

The volumetric gamma hea t ing rate inc ident upon a p a r t i c u l a r lamination,

and the gamma energy cu r ren t pe r u n i t area inc ident upon the j - t h Qoi j ) ,

are re l a t ed by the following equation. qo(l )y

lamination

qo(3) = Qo(j , /h(J) There fore

( 18b) Qo(j + 1) These two methods are i n f a i r 1 ince the va lues for the var ious material cons tan ts were not w e l l f ixed a t th i s po in t i n the

design f o r the reactor room w a l l , the second method o f eva lua t ing t h e

inc ident volumetric gamma hea t ing rate was usedin t h i s study.

second method i s simpler t o use and easier to ca l cu la t e .

The

The equations f o r the s teady-s ta te temperature drops ac ross each of

t he material laminations on the reactor s i d e o f t he a i r channel are given

below and the temperature po in t s are as i l l u s t r a t e d i n Fig. 2.

where

q* E hea t conduction rate ou t o f t he r eac to r room, Btu/hr*ft?,

E gamma hea t deposi t ion rate i n the s t a i n l e s s steel o u t e r skin, QS

Btu/hr*f?,

Ls = thickness o f t h e s t a i n l e s s steel skin, f t , and

= thermal conduct ivi ty o f t h e s t a i n l e s s s t e e l skin, Btu/hr*ft*’F. kS

13

TL - Ta = (cp + 4,

kI ? (20)

where the subscript I refers to the insulation lamination shown in Fig. 2.

: %

(q* + q, + 41 + &LFS -T3.=

kFS Y (21)

where the subscript FS refers-to the first mild-steel gamma shield (on

the reactor side of the air channel).

% - T, = q* + q, + qI + qFS

h Y (22)

where

Ta = temperature of the air in-the channel, OF, and

h= convective heat transfer coefficient, Btu/hr=ft?*OF.

The ‘average convective heat transfer coefficient across the walls of the

air channel is evaluated in Appendix B, and the value off 5 was determined

for a mean temperature of from 130 to 150’F. It was assumed that the

gamma heating in the air channel is negligible. Equations 19, 20, 21,

and 22 were added and the resulting equation was solved for q*. The heat

conduction- rate’ out of the reactor room to the air channel, :.

(& - Ta) -‘qs 2 Ls LI

[o

Lps 1 1 .. J~+F+-+-

8 .I kFS h

q* E (23)

On the concrete side .of- the air channel, the value .of primary interest TV- ~ is the maximum temperature of the concrete, Tmax. This-temperature may be

-determined by using Eqs. 12 and 14, but the temperature of the steel-!

concrete interface, Tn, must be known before these equations can be used.

The simple conduction and convection’equations for the laminated wall on

the concrete side .of the air-channel .are given below.

Q - Ta 4 Qss + 4; + QR

h Y (24)

14 ~

. . r j

where

qss = gamma hea t depos i t ion r a t e i n t h e second mi ld-s tee l gamma sh ie ld ,

Btu/hr*ft? , = rate a t which the gamma hea t generated i n the concrete is

conducted back toward t h e a i r channel, B t u / h r - f e , and qr

QR = r ad ian t hea t t r a n s f e r rate between the walls of the a i r chan

Btu/hr f t? ,

‘I

where

t Stefan-Boltzmann constant

= 0.1714 x loa E = sur face emiss iv i ty of a i r channel wal ls , assumed t o the

same for both surfaces .

2 + yss)Lss kSS

% - % = . (26) ..

I n t h i s study, t he re is a poin t i n the concrete a t which t h e tempera- .I

t u r e o f t he concrete is a maximum.

the a i r channel s i d e of t h a t po in t w i l l be conducted toward the a i r channel;

t h a t is, i n the d i r e c t i o n o f decreasing temperature.

q’, may be ca l cu la t ed by eva lua t ing dT/dx i n the concrete a t x = 0, us ing

Eq. 13.

A l l of the gamma hea t generated on

This amount o f hea t ,

C

~- recognizing t h a t .

9; = kc dx ? dTI x = o where the subsc r ip t c denotes concrete. The r i g h t s i d e o f Eq. 28 is p o s i t i v e r a t h e r than negat ive because Eq. 27 makes p o s i t i v e conduction

i n the d i r e c t i o n from the a i r channel toward the concrete, but q; is

i

:

&Iii 5

15

to be made positive in the direction from the concrete ‘toward~the air

channel. Equations 24, 25, 26, 27, and 28 were combined to yield one

equation in which the only unknown is Q. The-value for T3 can be calcu-

lated from the equations for the reactor side of the-air channel.

where

B’ =

i ‘i.qB + 1)

+ (pl+-l+ 1. - e 11 . (294

The constants in Eq. 29a that have no identifying subscripts are understood

to be for concrete. Equation 29.is also a transcendental equation. There-

fore, a trial-andferror method .must be used to solve for &. Once ‘J& and

qk are known, % can be calculated by using Eq.- 25.

Calculational Procedure

Since the.calculation of certain of the desired quantities requires

that the value of other desired quantities be known, there is a certain

order in which the problem must be worked. For a particular case) -the

thickness of.each of the laminations in the wall is selectedi and the

inside (reactor room) and -outside (earth,or internal) wall -temperatures

are specified. The incident ganrna current and the temperature of the

coolant air are also specified.. The constants for the various -equations

are selected, and those used are given in Appendix C:

16

With the proper cons tan ts f o r each d i f f e r e n t lamination, Eq. 17 is

f i r s t used t o c a l c u l a t e t h e gama hea t depos i t ions i n each o f the sepa-

rate laminations (qs, qI, qFs, qss, and 9,). to c a l c u l a t e t h e conduction l o s s from the r eac to r room q*. The tempera-

t u r e drops and the i n t e r f a c e temperatures on the r eac to r s i d e o f the a i r

channel a r e ca l cu la t ed by using Eqs. 19, 20, 21, and 22. Equation 29 is

used t o c a l c u l a t e t he value of %, and then the value o f q

by using Eq. 25.

of & i s ca lcu la ted by using Eq. 126. Once the value of Ts is known,

Equation 23 is then used

is ca lcu la ted R Then q: i s ca lcu la ted by using Eq. 24, and the value

i s obtained by us ing Eq. 14, and the maximum temperature of the T max X

concrete is ca lcu la ted by eva lua t ing Eq. 12 a t x = xT max.

grad ien t (OF/ft) i n the coolant air .

A t t h i s point , i t is poss ib l e t o c a l c u l a t e t he v e r t i c a l temperature

This temperature gradient ,

where

Ua = bulk v e l o c i t y of coolant a i r , f t / sec ,

Pa

Lch C Pa

= dens i ty o f a i r , lb/ft?,

= width o f a i r channel (d is tance between steel laminations), f t , = s p e c i f i c hea t o f a i r a t constant pressure, Btu/lb*OF.

The temperature of the a i r a t the top of the channel,

where H = the v e r t i c a l length of t h e a i r channel i n f e e t .

The e n t i r e c a l c u l a t i o n a l procedure can now be repeated using t h e

new a i r temperature a t t he top of the a i r channel, Ti. of the temperature o f the a i r a t the top o f t h e channel is necessary

because a higher T causes the maximum temperature of the concrete t o be

higher, and the magnitude of t h i s maximum temperature is one of the

c o n s t r a i n t s i n t h i s study.

This ca lcu la t ion

a

A program was developed f o r t he CDC 1604-A computer t o solve Eqs. 8

through 31 f o r the s teady-s ta te condition. The TSS (Thermal Shie ld Study)

17 z

LJ

4

b f

computer program is described in Appendix D. The program performs the

calculations in the order described above, and it will handle up to five

material laminations (excluding the air channel) in the proposed reactor

room wall and up to eight energy groups for the incident gamma current.

Transient Case

The problem of the loss of coolant for the reactor room wall is

basically a transient heat conduction problem with internal heat genera-

tion. If the flow of coolant air through the channel in the wall is lost

for an appreciable length of time, the temperature in the concrete and/or

the steel laminations may become excessive. To investigate this situation

with the goal of obtaining a first approximation of the amount of time

that such a loss of air flow could be sustained safely, a finite differ-

ence approach was taken.- The differencing is with respect to time and

the superscript n in the following equations denotes values after the

n-th time interval.

The proposed configuration of the reactor room wall was broken into

segments of given lengths with nodal points located.at the center of each

segment, as shown in Fig. 3. Each segment in the concrete region of the

wall was assumed to be 1 ft thick, each segment in the mild-steel gamma

shields and in the firebrick insulation was assumed to be 1 in. thick,

the entire stainless steel skin was treated’as a single segment l/16 in.

thick, and the air channel was treated as a single segment 3 in. thick.

The energy balance for a particular segment can be expressed seman-

tically as follows. The heat~conducted into a segment during the time A0

plus the heat generated in then segment during the time A6 equals the heat

stored in the segment during the time A6 plus the heat conducted out of the

segment-during the time A0. The corresponding algebraic equation for a

typical segment of the composite wall 5s given below with Segment 4

selected for illustrative purposes. ‘,

kCA +TSn -

W=ccp G.“) +q+= ne ?T4 n+l- kCA

T4n) + +T4” - %“I* C C

(32)

18

ORNL O r g 6T-12002 /STAINLLSS STELL \ SKIN

FIREBRICK < INSULATION FIRST MILD-STEEL < BAMYA SHIELD

r ( A I R CHANNEL

SECOND MILD-STEEL GAMMA SHIELD

CONCRETE

i 0 z

I1

f CURRENT + NODAL 1 W I N 1

I I

. .

6 4

. . .

5 9 1 SEGMENT ZC I I7 16 I!

Fig. 3. Designations Given Segments of Reactor Room Wall for Study of Transient Conditions.

Rearranging Eq. 32,

A characteristic equation at an interface between two different materials is given in Eq. 34.

- k A0 % s- c

l+" + 1 ksm (Gn - T7n) + Gn - T79 + L c , p sLsLcCp S s 8 Ps - qn + p L Z C

6 s Ps ( 3 4 )

where the subscript s denotes the stainless steel skin, the subscript'c denotes the concrete, and ks-C is an equivalent conductivity given by

-

where the subscripts a and b refer to any two adjacent materials,

19

Eighteen equations similar to those just given were derived to carry

the analysis across the entire reactor room wall , and a simple computer

program was written to perform the calculat ions required for one spec i f i c

transient condition.

I \

*

hd 20

i.

4. PARAMETRIC STUDIES

The parametric s tud ie s of t he proposed configurat ion of a laminated

wal l f o r the r eac to r room, shown i n Fig. 2, t o p ro tec t the concrete bio-

l og ica l sh i e ld from the gamma cu r ren t wi th in the room were made f o r two

conditions: t he s teady-s ta te condi t ion and the t r a n s i e n t condi t ion.

Parametric s tud ie s of t he material laminations f o r the s teady-s ta te con-

d i t i o n were made t o determine whether o r not

1. t h e bulk temperature of the concrete por t ion of the wal l could be

maintained a t l e v e l s below 212'F,

the temperature d i f f e r e n t i a l i n the concrete could be maintained a t

less than 40°F, and

2.

3. the conduction loss f o r a r eac to r room could be maintained a t 1 Mw

o r l e s s .

A t r a n s i e n t condi t ion was inves t iga ted t o determine t h e length of time

over which the loss o f coolant a i r flow could be t o l e r a t e d before t h e

temperature of the concrete would exceed the maximum allowable tempera-

t u r e o f 212'F.

Cases Studied f o r Steady-State Condition

For the parametric ana lys i s of the composite plane w a l l wi th i n t e r n a l 3:

heat generat ion f o r s teady-s ta te condi t ions, the a i r channel was not con-

s idered as a mater ia l lamination but r a t h e r a s having a f ixed width of

3 in . between the f i r s t and second mi ld-s tee l gamma sh ie lds .

t u r e of t he incoming cool ing a i r a t the bottom of the a i r channel was

assumed t o be 100°F, and the ve loc i ty of the a i r w a s set a t 50 f t l s e c .

The thickness o f t he s t a i n l e s s steel skin on the r eac to r s i d e o r i n t e r i o r

sur face of t he w a l l was f ixed a t 1/16 in., and t h e temperature of the

i n t e r i o r sur face of the reac tor room wall was considered t o be uniform

over the sur face and constant a t 110O0F.

i n Chapter 3 were used with the TSS computer program descr ibed i n

Appendix D t o examine the s teady-s ta te e f f e c t s o f changing the

The tempera-

Equations 8 through 31 derived

,

i

c; ?

21

1. thickness of the firebrick insulation,

2. total amount of mild steel used for the gamma shields,

3. ratio of the amount of~steel on the reactor side of the air channel

to the amount of steel on the concrete side of the air channel,

4. thickness and outside temperature of the concrete wall, and the

5. magnitude of the incident monoenergetic (1 Mev) gamma current.

Sixty-four separate cases were analyzed for the steady-state con-

dition to determine the effects of changing those parameters of interest.

Data illustrative of the typical effects of varying the parameters were

selected from the results of these analyses and are compiled .in Tables 1

through 7. The effects of changing the parameters are given for.incident

gamma currents of 1 x 10’s and 2 x 10la bhotons/cn? *set in all of these

tables, and the conditions at the bottom (entrance) and top (exit) of

the air channel are given for both magnitudes of incident gamma current.

For cases with an incident gamma current of 1 x 1012 photons/cu?*sec,

the maximum temperature of the concrete increases approximately 50°F from

the bottom of the air channel to the top. For cases‘with an incident

gamma current of 2 x 101s photons/ca?*sec and no conduction back to the

reactor room, the maximum temperature of the concrete increases approxi-

mately 80°F from the bottom to the top of the air channel. For a given

gamma current and insulation thickness, the conduction loss changes very

little (about 0.04 Mw)between the bottom and the top of the air channel,

The largest value for the maximum temperature of the concrete at

the top of the air channel in those cases with an incident gamma current

of 1 x 101s photons/cn?*sec and an insulation thickness of 5 in. or more

is approximately ZOOoF, On the other hand, the smallest value for the

maximum temperature of the concrete at the top of the air channel in

those cases with an incident gamma’current of 2 x 10la photons/& *set

and an insulation thickness of 5 in. or more is greater than 250’~.

22

Table 1. Results of Investigation of First Steady-State Case

Case Conditions Studied Lc = 8 ft Tg = 50°F To = llOO°F

Ls = 1/16 in. $ = 5 in. Ss = 4 in. Lss = 2 in.

0, P 1 x Ida photons/& -see 4, o 2 X le8 photons/d *bee Bottom of Top of Bottom of Top of Channel Channel Channel Channel 16.57 75.47 370.6 11.69 33.65 25.84 110.6 0.5812

1099.9 247.9 240.5 100 .o 129.6 129.8

0.1018 852.0 7.412 140.5 29.63 0.216

140.5 0.5422 1.104

16.57 75.47 370.6 11.69 33.65 22.04 131.2 0.5382

1099.9 297.1 289.9 153.0 186 60

186.2

0.0946 802.8 7.185 136.9 32.98 0.1916

193.6 0 .&83 1.103

33.14 33.14 151.0 151.0 741.2 741.2 23.38 23.38 67.30 67.30 55.31 48.99 198.9 253.9 0.3520 0.2838

1099.9 1099.9 324.6 402.7 314.1 392 5

100 .o 184.0 155.5 249.3 156 .O 249.7

0.0679 0.0565 775.3 697.3 10.55 10.19 214.1 208.5 55.52 65.25 0.4554 0.4148

181.3 268.5 0.6343 0.4887 1.751 1.777

- .?

w .

c; i

23

Table 2. Results of Investigation of Second Steady-State Case Case Conditions Studied

To = llOO°F Lc = 3 ft T6 = 70°F

La = 1/16 in. LI = 5 in. LFS = 4 in. Lss = 2 in.

0, = 1 X lea photoncl/cn? rsec 0, a 2 X lea photons/d -8ec Bottom of Top of Bottom of Top of

Channel Channel channel Channe 1 16.57 16.57 75.47 75.47 370.6 370.6 11.69 11.69 33.65 33.65 18.33 8.446 111.6 133.3 0.5812 0.5385

1099.9 1099.9 247.9 296.7 240.5 289.5 100.0 152.6 128.3 183.3 128.5 183.4

0.1018 0.0947 852.0 803.2 7.412 140.5

33.14 151.0 741.2 23.38 67.30 42.64 200.8 0.3520

1099.9 324.6 314.1 100 .o 153.4 153.7

0.0679 775.3 10.55 214.1

33.14 151.0 741.2 23.38 67.30 26.19 258.2 0.2845

1099.9 402.1 391.9 183.4 244.9 245.2

0.0566 697.9 10.19 208.5

28.32 30.68 53.36 60.55 0.1678 0.1043 0.3740 0.2683

133.4 184.4 167.4 250 .o 0.3124 0.1276 0.3878 0.2061

24

Table 3. Results .of Investigation of Third Steady-State Case

Case Conditions Studied To = 1lOOOF L~ 8 ft TU = 50°F

I

L, = 1/16 in. 5 = 5 in. $s = 2 in. Lss = 4 in.

0, E 1 X Id2 photonr/cl$ -rec 0, = 2 x le2 photons/crdaarec Bottom of Top of Bottom of Top of Chainel Channel Channe 1 Channel 16.57 75 147 299.6 82.69 33.65 25.15 87.31 0.5960

1099.9 230.9 227.5 100 .o 139 .O

140.1

0.1043 869 .O

3.452 127.5 39.03 1.028

1m.1 0.5139 1.081

16.57 75.47 299.6 82.69 33.65 21.50 1002.6 0.5538

1099.9 279.2 275.9 151.9 193.3 194.2

0.0972 820.7 3.341 124.0 41.35 0.9814

201.2 0.3927 1.074

33.14 151.0 599.2 165.4 67.30 54.08 141.5 0.3799

1099.9 292.7 288.0 100 .o 172.2 174.3

0.0276 807.2 4.754 188 .O

72.19 2.105

198.2 0.6004 1.689

33.14 151 .o 599.2 165.4 67.30 48.21 177.6 0.3139

* 1099.9 368.2 363.6 181.1 259.3 261.4

0.0616 731.7 4.580 182.5 78.24 2 .om 279.5 0.4745 1.694

25

Table 4. Results of Investigation of Fourth Steady-State Case Care Conditions Studied

To = llOO°F Lc P 3 ft Te = 70°F

Ls = 1/16 in. LI = 5 in. LFS = 2 in. Lss = 4 in.

4,, = 1 X lea photone/ca? osec e,, = 2 X lOla photone/ca? -set Bottom of Top of Bottom of Top of Channel Channel Channel Channel

q,, Btu/hr'fe 16.57

qFsO Btu/hr* fl? 299.6 qss, Btu/hr-f@ 82.69 qcO Btu/hr*fP 33.65 qc ' 9 Btu/hr*ft? 16.53 qRO Btu/hr*fP 88.49 HWL, Mu 0.5960

1099.9 T10 F h8 OF 230.9 6, OF 227.5

100 .o 137.5 t r F

b r F 138.5

%-T10 OF 0.1043 T1-Tar 9 869 .O

%-Tar OF 3.452 ~ 3 0 ~ a 0 OF 127.5

6-%, F 0.9178

T-0 OF 142.4

qIO Btu/hr*fI? 75.47

0

0

0

0

Tar F

%-Tar OF 37.54 0

16.57 75.47 299.6 82.69 33.65 7.048 104.9 0.5543

1099.9 278.8 275.5 151.4 190.4 191.2

0.0973 821.1 3.342 124.0 38.93 0.7963

192.8

33.14 151.0 599.2 165.4 67.30 39.42 143.8 0.3799

1099.9 292.7 288 .O

100 .o 169.7 171.6

0.0726 807.2 4.754 188 .O

69.71 1.917

183.1 0.3454 1.673

33.14 151.0 599.2 165.4 67.30 24.17 182.4 0.3146

1099.9 367.5 362.9 180.3 254.7 256.4

0.0617 732.4 4.581 182.6 74.40 1.722

260.5 0.1881 1.669

x T m l a x 8 ft 0,2724 0.1052 D/H0 OF/ft 1.072 1,058

26

Table 5. Results of Investigation of Fifth Steady-State Case Case Conditions Studied

To 6 llOO°F Lc = 8 ft T6 3 50°F

La = 1/16 in. 5 = 5 in. LFS = 2 in. Lss = 2 in.

(b P 1 x le3 photons/cu? -see @o = 2 x lo1* photons/& OBec Bottom of Top of Bottom of Top of Channel Channel Channel Channel

qs, Btu/hr'ft? 16.57 16.57 33.14 33.14

q*s, Bm/hr*f? 299.6 299.6 599.2 599.2 qss, Btu/hr*f@ 71.15 71.15 142.3 142.3

@ Btu/hr*ft? 35.90 32.24 75.58 69.71 qR, Btu/hr'fP 87.42 102.7 141.7 177.9 W J MW 0.5960 0.5538 0.3799 0.3141

qI, Btu/hr*f3 75.47 75.47 151.0 151.0

qc, Btu/hr*fe 45.19 45.19 90.38 90.38

qc 8

1099.9 1099.9 230.9 279.2 227.5 275.9 NO .o 151.9 138.9 193.1 139.4 193.6

1099.9 292.7 288 .O

100 .o 171.9 173.0

1099.9 368.1 363.6 181.0 259.0 260.1

0.1043 0 %-T1, F T1-%8 OF 869 .O

%-6, OF 3.452 TS-T,, OF 127.5 t o T ~ 8 OF 38.89 T g ' t , OF 0.5353

T-8 OF 155 .O

xr alax, ft 0.5851 AT/& OF/ft 1.080

0.0972 820.7 3.341 124.0 41.22 Q.5118

205.6 0.4716 1.073

0.0726 807.2 4.754 188 .O

71.92 1.095

208.6 0.6638 1.688

0.0616 731.8 4.580 182.6 77.39 1.057

289.1 0.5484 1.692

Table 6. Results of Investigation of Sixth Steady-State Case

Case Conditions Studied

To = l1OOOF Lc = 8 ft '& = 50°F

L~ = 1/16 in. LI = 7.5 in. LFS = 4 in. Lss = 2 in.

e,, = 1 X lOla photons/cu? esec 4o = 2 X lOla photons/d ~sec Bottom of Top of Bottom of Top of Channel Channel Channe 1 Channel 16.57 111.9 338.1 10.69 30.70 23.47 86.60 0.2891 1

1099.9 223.2 217.2 100.0 124.1 193.6

0.0529

16.57 111.9 338.1 10.69 30.70 20.35 101.1 0.2649

1099.95 265.1 259.2 144.0 170.5 170.6

0.0488

33.14 223.8 676.2 21.38 61.40 50.39 164.5 0.0245

1099.99 297.9 288.7 100.0 147.2 147.7

0.0131

Tl-%D OF 876.7 834.8 802.1 % - % 9 OF 6.060 5.9 5

b-T,, F 117.2 115.2 7 0

qCT,D OF 24.10 26.42 47.24 % - % I OF 0.1965 0.1764 0.4150

134 .o 177.6 170.7

27

28

Table 7. Results of Investigation of Seventh Steady-State Case Care Conditions Studied

To = llOO°F Lc = 8 ft & = 5O0F

La = 1/16 in. 5 = 10 fn. LFS = 4 in. Lss = 2 in.

0, = 1 x lea photons/ca? =see 0, E 2 X 10la photons/& =rec Bottom of Top of Bottom of Top of Channel Channel Channel Channel

q,, Btu/hr*fi? 16.57 16.57 33.14 qI, Btu/hr*ft? 146.7 146.7 293.4 qFs, Btu/hr-ft? 307.1 307.1 614.2

qc, Btu/hr*f@ 27.89 27.89 55.78 qsss B-u/hr*f@ 9.689 9.689 19,38

Tan OF 0

t r F

21.08 73.58 0.1118

1099.98 208.6 203.3 100 .o 120.9 121.0

0.0232 891.4 5.304 103.3 20.87 0.1769

129.6 0.5256 0.8064

18.35 84.92 0.0955

1099.98 245.9 240.7 138.7 161.3 161.5

0.0205 854.1 5.218 102.0 22.59 0.1594

167.6 0.4117 0.8088

_ _ e

W

33.14 293.4 614.2 l9.38 . 55.78

6, 29

i Tables 1, 6, and 7 may be compared for the effects of changing the

thickness of the firebrick insulation from 5 in. to 7.5 in. and 10 in.

The addition of 2.5 in. of insulation decreases the conduction loss by

about a factor of 2, and this addition also decreases the maximum temper-

ature of the concrete by approximately 15’F in those cases with an inci-

dent gamma current of 1 x 10la photons/ca?*sec.

Tables 1 and 5 may be’compared for the effects of changing the

total thickness of the steel in the two gamma shields. Decreasing the

total thickness from 4 to 2 in. causes only a slight increase in the

conduction loss. The maximum temperature of the concrete is increased

approximately lOoF for the cases with an incident gamma current of 1 x 10la

photons/ca?*sec and by approximately 20°F for the cases with an incident

gamma current of 2 x 1012 photons/en? *sec.

Tables 1 and 3 and Tables 2 and 4 may be compared for the effects of

changing the ratio of the thickness of the steel on the reactor side of ;

the air channel to the thickness of the steel on the concrete side of the

air channel. Changing from 4 in. on the reactor side and 2 in. on the :

concrete side to 2 in, on the reactor side and 4 in. on the concrete side

increases the conduction loss only slightly and increases the maximum

temperature of the. concrete approximately lOoF.

Tables 1 and 2 and Tables 3 and 4 may be compared for the effects of

changing the thickness of the concrete and the temperature over the out-

side surface of the concrete wall; Changing the thickness of the concrete -

from 8 to 3 ft and the temperature on the outside surface from 50 to 700F

decreases the maximum temperature of the concrete about 1OoF but the

conductian loss is not affected appreciably,

Case Studied for Transient Condition

Eighteen finite difference equations, with the differencing with

respect to time, similar : to Eqsi 32 through 35 discussed in Chapter 3

iid were written-to analyze the proposed configuration of the reactor room

wall for one transient-condition case, The analysis was performed to i

30

determine the length of time over which a loss of coolant air flow could be tolerated before the temperature of the concrete would exceed the maximum allowable temperature of 212'F. could arise as a result of a malfunction in the blower system supplying the coolant air. Although natural convection currents would cause some cir- culation of the coolant air during 8 blower failure, it was assumed that

Such a loss of coolant air flow

the coolant air was stagnant during the failure so that the worst case could be analyzed. as an insulating material and removes no heat from the wall.

Under this assumption, the air channel serves only

The conditions established for the analysis of this particular case were a S-in.-thick layer of firebrick insulation, a 4-in.Othick layer of mild steel for the first gamma shield, the 3-in.-wide air channel, a 2- in.-thick layer of mild steel for the second gamma shield, and a 6-ft- thick concrete wall for the biological shield. A simple computer program

t

was written to perform the calculations, but the zero-time temperatures and heat depositions for each segment in the composite wall were calcu- lated by hand and used as fixed numbers in the program. This computer program was used only to obtain a first approximation to the transient situation for one particular case, and the details of the program are not presented here.

The program was run for elapsed times of t = 1.0 hr, t = 2.0 hr, t = 3.0 hr, t = 4.0 hr, and t = 5.0 hr for the condition of internal heat generation (reactor at power during blower failure) during the transient

period. elapsed times but

for the condition of no internal heat generation (reactor shutdown simultaneous with blower failure) during the transient period. The computer program used to analyze the condition for internal heat genera- tion is given in Table 8. generation, Q2C through Ql9SS in Table 8 are set equal to zero. The resulting temperature distribution in the proposed reactor room wall analyzed for the condition of internal heat generation during the transient period is shown in Fig. 4, and the temperature distribution in

The program was then run again for the same

To analyze the condition of no internal heat

-

the wall with no internal heat generation during the transient period is

illustrated in Fig. 5.

hd

-- P

cbt

i

.

,

31

Table 8. Cdmputer Program Used to Analyze the Proposed Reactor Room Wall for the Condition of Internal Heat Generatfon

32

Table 8 (continued)

4

33

ORNL Dug. 67-12003 soa

roa

L

200

IO0

LEQENO - @ TEMPERATURE DISTRIBUTION AT 1. 0.0 HRS.

@ TEMPERATURE DISTRIBUTION AT 1. 1.0 HRS. @ TEMPERATURE DISTRIBUTION AT 1. 2.0 HRS.

@ TEMPERATURE DISTRIBUTION AT T 8 3.0 HRS.

@ TEMPERATURE DISTRIBUTION AT T 4.0 HRS. @ TEMPERATURE DlStRlaUTlON AT T 5.0 HRS.

30 35 40

g. 4. Temperatu bution in Proposed Reactor Room Wall rnal Heat Gene ient Period.

te Maintained During Loss-of-Wall-Cool-

I-) .

34

80f

400

- L 0

u -

soa L U .. s U t

200

I O 0

1 111

I LEGEND

ORNL 0- 8 T - I L D M II 6 TEMPERATURE OlSTRlBUTlON AT T 0.0 HRS. @ TEMPERATURE OISTR18UTION AT T 1.0 HRS. @ TEMPERATURE OlSTRlBUTlON AT t 0.0 HAS. @ TEMPERATURE DISTRIBUTION AT t S.0 HRS.

@ TYPERATORE OISTRIBUTION AT t 4.0 WRS. 0 TEMPI

WALL THICKNESSES t INCHES 1

Fig . 5. With No Transient Period.

Temperature Distribution in Proposed’Reactor Room Wall Internal Heat Generation During the Loss-of-Wall-Coolant

! i

35

5 . CONCLUSIONS

Two bas i c conclusions may be drawn from the r e s u l t s of the parametric

s.tudies made i n t h i s i nves t iga t ion of the proposed configurat ion of a

laminated wall t o p ro tec t the concrete b io log ica l sh i e ld from the gamma

cur ren t wi th in the room housing a 250-Mw(e) molten-salt breeder r eac to r , a

fue l - sa l t - to -coolant -sa l t heat exchanger, and a blanket-sal t - to-coolant-

s a l t heat exchanger.

as the wa l l coolant, the proposed configurat ion i s acceptable f o r an

inc ident monoenergetic (1 MeV) gamma cur ren t of 1 x lola photons/cn?*sec

f o r a l l cases considered i n which the thickness of the f i r e b r i c k insu la-

t i o n was 5 in . o r more. A second bas ic conclusion i s t h a t t he proposed

configurat ion is not acceptable f o r those cases considered with an

inc ident monoenergetic (1 MeV) gamma cu r ren t o f 2 x 1 O l 2 photons/ca? .sec

because the maximum allowable temperature of the concrete (212OF) i s

exceeded by 50 to 100°F. The values o f severa l of the parameters of

i n t e r e s t i n t h i s study t h a t were obtained from the cases analyzed f o r

a gamma current o f 1 x 10'' photons/cnP*sec a r e given i n Table 9 .

The f i r s t bas i c conclusion i s t h a t with a i r used

a

Based on the assumption t h a t the f l o o r and c e i l i n g o f the reactor room

have the same laminated configurat ion as the walls, giving a t o t a l llwallll sur face a r e a of 8276 f ? , the proposed w a l l configurat ion w i l l al low the

conduction l o s s from the r eac to r room t o be maintained a t a l e v e l below

1 Mw if the thickness o f the in su la t ion i s 5 in . or more.

based on an a i r velo c and an a i r coolant channel width

o f 3 in. , a i r i s an acceptable

Further,

m f o r cool ing the wal l .

A general conclusion t h a t may be drawn from the l imi ted a n a l y s i s

made o f one t rans ien t -condi t ion case i s t h a t i f the ambient temperature

of t he r eac to r room rema a t approximately llOO°F, the proposed con-

f igu ra t ion of the reac to om w a l l s tudied i n t h i s case can s u s t a i n a loss o f coolant a i r flow under the condi t ions described i n Chapter 4 f o r

approximately 1 hour bef

exceed 212'F. I f a zero a current is assumed, the

llpermissiblell loss-of-coolant-air time i s g r e a t e r than one hour but less

than two hours.

re. of the concrete begins t o

t i

. . .

.

Table 9. Range o f Parameters of I n t e r e s t i n Studies Made of Proposed Wall With An Inc ident Gamma Current of 1 x lora photons/ct#*sec

Parametric Conditions Variable o f Minimum Maximum LI 5 s Lss Lc li3

I n teres t Value Value (in.) (in.) ( in.) ( f t ) (OF) Skin AT,'F 0.021 10 4 2 a a

0.22 2.5 2 4 . a a Insu la t ion

AT, OF

F i r s t steel sh ie ld AT, F

726 2.5 4 2 906 10 2 a

2.38 10 2 a 10.9 2.5 4 2

Second steel 0.08

A i r v e r t i c a l tempera- 0.77

sh ie ld AT, OF

t u r e gradient , OF/ft

F

(Q12'F)

0 Tc max' 124

f t T max, X

(Tmax < 212'F) 0.11

m, Mw 0.096

8 a a a

50 a a a

1.1 2.5 4 2 2.5 2 4

3 70 8 50

10 2 2 3 70 1.57 2.5 4 2 8 50

10 4 2 3 70

205.6 5 2 2 8 50

5 2 4 3 70 0.58 7.5 2 2 8 50

10 4 2 8 50 1.32 2.5 2 a a a

This parameter has l i t t l e e f f e c t i n combination with the o t h e r a

the values of the va r i ab le s of i n t e r e s t are e s s e n t i a l l y the same f o r parameter .

~-

parameters given, var ious values of

w OI

and t h i s

e: .

j .

37

If a wall of the type proposed is used, the temperature of the con- or the conduction loss, or both, can be controlled to some

TC’ Crete, extent by varying the physical characteristics of the wall. of the insulation can be increased, but the desirable effect approaches a limit rather rapidly. As the results of our parametric studies have indicated, an insulation thickness can be reached that will cause con- duction back into the reactor room. The total thickness of the mild- steel gamma shields can be increased with good results up to the point where the gamma current is reduced by several orders of magnitude.

The thickness

After this point is reached, adding more steel for gamma shielding does not produce sizable changes in the maximum temperature of the concrete. A total of approximately 6 in. of steel is sufficient for an incident monoenergetic (1 MeV) gamma current of 1 x 10” photons/cu?*sec. The thickness of the mild-steel gamma shields should be arranged so that the major portion of the steel is on the reactor side of the air channel. Placing the major channel results in the undesirable effect of raising the maximum tempera- ture of the concrete. within the reactor room that may be causing a large gamma current appears to be a better solution than increasing the thickness of the wall laminations for gamma currents greater than 1 x 10la photons/ca?*sec.

When sufficient information becomes available, an overall energy

portion of the steel on the concrete side of the air

Shadow shielding of the particular components

balance should be written, starting with the fissioning process in the reactor and extending out through the wall of the reactor room to an outside surface. a conduction loss of 1 Mw will permit maintenance of the desired ambient temperature within the reactor room without the addition of auxiliary cooling ar heating systems.

This balance i s necessary to determine whether or not

39

APPENDICES

41

Appendix A

EQUATIONS NECESSARY 'ID CONSIDER A MULTIENERGETIC GAMMA CURRENT

The equations derived in Chapter 3 of this report were based on the assumption that the incident gamma current is monoenergetic. energy distribution of the incident gamma current is known, this curr,ent can be represented as a multigroup current. incident multigroup gamma cur must be written to account fo multigroup modification has been made in the following equations, and they are to be used in place of the correspondingly numbered equations in Chapter 3 when the energy distribution of the gamma current is known. The subscript i denotes the energy group, and the terms are defined in Appendix E.

If the

The equations in which an nt appears, either directly or indirectly, this segmentation in gamma energy. This

(A.9a)

42

,

dT 1 - = -(T - To) dx L L

PiX(cri - 1) + (1 - Ai)e 'T = ',pie e

= = Qj + li = (QO(j), - Sji) Q j + l i i

J

(A. 13)

(A. 14)

(A. 16)

(A. 17)

(A. 18)

(A. 18a)

(A. 18b)

1 (CJ 44 + Q( + - + - Lss k Lc ) kSS c

i

where

44

Appendix B .

EVALUATION OF THE CONVECTIVE HEAT TRANSFER COEFFICIENT

The average convective heat transfer coefficient, h, for the walls of the air channel was evaluated ~~ by using the expression published by Kre i th .

k h = 0.036 E Re: *8pS /3 , where

0 k = thermal conductivity of air, Btu/hr*ft* F, H = vertical length of the air channel, ft,

ReH = Reynolds number evaluated at the top of the air channel, and Pr = Prandtl number evaluated for air.

The Reynolds number evaluated at the top of the air channel,

. - - where

U = the bulk air velocity, ft/sec, p = density of the air , lb/ft?, and

= viscosity of air, lb/ft*sec. The Prandtl number evaluated for air,

where C = the specific heat of air at a constant pressure, Btu/lb*OF. In the range of temperatures considered, Pr is- approximately constant and equal to 0.72. Kreith'2 expression for h air-wall mean temperatures in the air channel, and the results are on the following page.

P

was evaluated for various

lFrank Kreith, p. 286 in Principles of Heat Transfer, International Textbook Company, Scranton, Pennsylvania, 4th printing, 1961.

I 45

- T

100 130 150

0 .h

(Btu/hr*ft? 'OF) 5.15 5.04 5.04

The mean temperature of the walls of the air channel is expected to be approximately 130 to 150°F, and a value of 5 was used for the convective heat transfer coefficient at the walls of the air channel.

i

i

46

Appendix C

VALUES OF PHYSICAL CONSTANTS USED IN THIS STUDY

Values for the gamma energy attenuation coefficient, %, the t o t a l gamma rttenuatiou coefficient, p, and the dimensionless constants a, @, and A used i n the Taylor buildup formula for a gamma energy of 1 Hev are tabulated belov.

P a Material L(ft-11 (ft-1) p %?

Type 347 atainleas 6.28. 14.0ab 0.0895' 0.04C aC steel

Kaolin insulating 0.367' 0.83Sd 0.088' O.02gd lod - brick

Mild steel 6.30. 14.02. 0.0895' 0.04C BC Concrete 1.99d 4.55d 0.0886 0.029' lod

Values for the density, p # Specific heat, c thermal COndUCtiVitp, k, ant equivalent P'

thermal conductivity at interfaces of adjacent materials, E, for materiala in the proposed laminated wall i n t he i r order of occurrence from the reactor outward are tabulated below.

1

0 lbm/ft3)

Material l & a ( Type 347 rtain- 7.Bb b86.gb

Kaolin insulat- 0.433' 27.03e

Mild steel 7.83b uq.ab

less s t e e l

lag brick

A i r 0.060e

Mild steel 7.83b 488Ab

0 .29 0.15" 0.159

0.298 0.11e 26.0e

0.241e 0.0174e 0.0232

0.0232 0.lP 26.0'

0.584 Concre re 2.3Sd 146.7d 0.20e 0 . W

*E. P. Blizard and L. S. Abbott, editors, p. 107 i n Reactor Handbook, Vol. S, Part B, Johh Uiley and Sons, New York, 1962.

bM. M. El-Uakil, p. 223 i n Nuclear Power Engineering, McGraw-Hill Book C~IU~UII~, be., F i r s t Edition, Nev York, N w York, 1962.

%. P. Blizard md L. S. Abbott, editors, p. 116 in Reactor Randbook, Vol. S, Part B, John Wiley md Sons, New York, 1962.

dnReactor Physics Constants," USAEC Report ANL-5800, Argonne National Laboratory,

'Frank Kreith, pp. 533-535 in Principles of Heat Transfer, International Textbook

pp. 653-6578 July 1963.

Company, 4th printing, Scranton, Pennsylvmia, 1961.

c

47

Appendix D

TSS COMPUTER PROGRAM

A program-was developed for the CDC 1604-A computer to solve the

equations-(Eqs. 8 through 31) necessary to evaluate the proposed con-

figuration of the reactor room wall for the steady-state conditions. As

writ ten, the TSS (Thermal Shield Study) program will handle up to five

material laminati.ons, excluding the air channel, and up to eight energy

groups for the incident gamma current. The calculations are performed

in the order described in Chapter 3. For a problem with five energy

groups and sixteen different combinations of laminations (cases), the

machine time is one minute and 45 seconds and the compilation time is

56 seconds.

A Newton-Raphson iteration scheme is used to evaluate & and xT max,

The convergence criterion for Q is that the right and left sides of

Eq. 29 must agree to within 0.05, and the criterion for xT max is that the

right and left sides of Eq. 14 must agree to within 0.10. These conver-

gence criteria could be made smaller with a corresponding increase in

machine time, but very little more real accuracy would be obtained be-

cause the program uses the approximate method to calculate the incident

gamma current at each material interface. If more real accuracy is

required, the program c0ul.d be modified to calculate the attenuated gamma

current.at each ,interface and to calculate from this information the

incident gamma current at the material interfaces.

If a vertical temperature profile were known for the interface of

the reactor room and the skin,~the program could be modified to do calcu-

lations at several points up the air channel rather than just at the top

and bottom as it does at present. Both the setup of the program and the

manner in which the necessary input data are prepared-are explained in

the following discussion.

The TSS computer program is set up for a given physical situation

with a given photon current incident upon the reactor room wall. The

temperature of the inside surface of the wall is fixed at a given value.

. .

48

. The composite w a l l is composed of f i v e mater ia l regions, and progressing

from the in s ide surface outward, these regions are (1) a t h in steel skin,

(2) an in su la t ing mater ia l , (3) the f i r s t steel gamma sh ie ld , (4) t h e

second steel gamma shield, and (5) the concrete b io log ica l sh i e ld with a

f ixed temperature on the outs ide surface. The 3-in.-wide a i r channel

placed between the f i r s t and second gamma sh ie lds i s not considered a

material region. By ca l cu la t ing a v e r t i c a l temperature grad ien t i n the

a i r channel, the program w i l l c a l cu la t e a t both the bottom and top of

the r eac to r room wall the

1, 2.

gamma hea t generation r a t e i n each mater ia l ,

temperature a t each mater ia l i n t e r f ace and temperature changes across

each mater ia l ,

conduction hea t l o s s from t h e r eac to r room t o the a i r channel, r ad ia t ion heat t r a n s f e r rate between the w a l l s of the a i r channel,

hea t i n the concrete conducted both toward and away from t h e a i r channel, and the

maximum temperature i n the concrete and i t s corresponding locat ion.

3. 4. 5 .

6 .

The program input deck allows the use of any material i n any region *

of the composite wall.

i n s ide wal l temperature, a f ixed i n l e t a i r ve loc i ty and temperature, and

fixed wal l mater ia ls , the ca l cu la t ion of a p a r t i c u l a r case i s done by

se l ec t ing a l l material thicknesses and the temperature o f the ou t s ide

surface of the concrete w a l l . A t present , t he program w i l l al low a maxi-

mum of 32 cases t o be run, but i t can e a s i l y be expanded t o handle more.

For a f ixed incident photon current , a f ixed

Preparat ion of Input Data

The f i r s t set of input da t a cons i s t s of energy-dependent information

per ta in ing t o the incident photon cur ren t and t o the nuclear p rope r t i e s

of the ma te r i a l s chosen f o r each region i n the wall .

the information is supplied i s given on the following page. The order i n which

- e

Ld *

m 49

&i 0 Card 1. Qslil), Q=(2), . ..> QSl(8). The incident photon current

(Btu/hr*ft?) for each of eight possible energy groups. 2. Card EMUl(l), EMLl1(2), . . . . EMIJl(8). The energy absorption

coefficient (l/ft) in the first region of the wall (the inner skin) for

s

each of eight possible energy groups. Card 3. AMUl(l), AMU1(2), . . . . AMul(8). The mass attenuation

coefficient (l/ft) 'in the first region of the wall (the inner skin) for each of eight possible energy groups.

Card 4. ALPHA(l), ALPHA1(2), . . . . ALPHAl(8). The dimensionless

constant Q used in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups.

Card 5. BETAl( BETA1(2), . . . . BETAl(8). The dimensionless con- stant 8.used in the Taylor buildup formula in the first region of the

wall (the inner skin) for each of eight possible energy groups. Card 6. Al(l), A1(2), . . . . Al(8). The dimensionless constant A used

in the Taylor buildup formula in the first region of the wall (the inner skin) for each of eight possible energy groups.

Card 7. EMlJ2(1), EMU2(2), . . . . EMU2(8). The same as Card 2 except for the second region of the wall (insulation).

Card 8. AMUP( AMU2(2), . . . . AMJP(8). The same as Card 3 except for the second region of the wall (insulation).

Card 9. ALPHA;!(l), ALPHA2(2), . . . . ALPHA2(8). The same as Card 4 except for the second region of the wall (insulation).

Card 10. BETA2(1), BETA2(2), . . . . BETA2(8): The same as Card.5 except for the second region of the wall (insulation).

Card 11. A2(1), A2(2), . . . . A2(8). The same as Card 6 except for the second region of the,wall (insulation).

Card 12. EMU3(1), EMU3(2), . . . . EMID( The same as Card 2 except for the third region of the wall-(the first gamma shield).

Card 13. AMU3(1), AMU3(2), ..,, AMU3(8). The same as Card 3 except for the third region of the wall (the first gamma shield).,

Card 14. ALPBA3(1), -ALPIiA3(2), .*., ALPHA3(8). The same as Card 4 except for the third region of the wall (the first gamma shield).

50

Card 15. BETA3(1), BETA3(2), ..., BETM(8). The same as Card 5 except

f o r the t h i r d region of the wal l ( the f i r s t gamma sh ie ld) .

Card 16. A3(1) , A3(2), .,., A3(8). The same a s Card 6 f o r the t h i r d

region of the w a l l ( t he f i r s t gamma sh ie ld) .

Card 17. EMU4(1), EMU4(2), ..., EMU4(8). The same as Card 2 except

f o r t he four th region of the w a l l ( the second. gamma sh ie ld) .

Card 18. AMU4(1), M 4 ( 2 ) , ..., AMU4(8). The same as Card 3 except

fo r the fourth region of the wal l ( t he second gamma sh ie ld) .

Card 19. ALPHA4(1), ALPHA4(2), ..., ALPW4(8). The same as Card 4

except f o r the fourth region of t he wal l ( t he second gamma sh ie ld) .

Card 20. BETA4(1), BETA4(2), . . . , BETA4(8). The same as Card 5

except f o r the fourth region of t he w a l l ( t he second gamma shield) . t

Card 21. A4(1), A4(2), ..., A4(8). The same as Card 6 except f o r

t he four th region of t he w a l l ( t he second gamma shield) .

Card 22. EMU5(1), EMU5(2), ..., EMU5(8). The same as Card 2 except

f o r the f i f t h region of the w a l l ( the b io log ica l sh ie ld) .

Card 23. AMU5(1), AMU5(2), ..., AMU5(8). The same as Card 3 except

f o r the f i f t h region of the w a l l ( the b io logica l sh ie ld) .

Card 24. ALPHAs(1); ALPHA5(2), ..., ALPHAs(8). The same as Card 4

except f o r t he f i f t h region of t he w a l l ( the b io log ica l sh ie ld) .

Card 25. BETAS(l), BETAS@), ..., BETAS(8). The same as Card 5

except f o r the f i f t h region of the w a l l ( t he b io log ica l shield) .

the f i f t h region of the w a l l ( t he b io logica l sh ie ld) .

Card 26. A5(1), A5(2), ..., A5(8). The same as Card 6 except f o r

The format statement fo r a l l of the above cards i s 8F9.0. Since

only the f i r s t 72 spaces on each d a t a card are used, t he las t e igh t may

be used f o r i d e n t i f i c a t i o n purposes. I f fewer than e igh t energy groups

are used, t he unused da ta f i e l d s may e i t h e r be punched w i t h a zero or

l e f t blank. I n e i t h e r case, the energy-summing DO loops subscr ipted

J, K, L, and N must be changed t o correspond t o the number of energy

groups used; t h a t is, i f there are s ix energy groups, DO 100 I = 1,6;

and K, L, and N a r e a l s o 1,6.

pond t o the number of energy groups used, d iv is ion by zero w i l l occur.

I f the DO loops are not changed t o corres-

* 51

The next s e t of da t a entered i s energy'independent and i s assumed

t o be constant over t he range of temperatures covered i n the program.

This information should be given on the two following cards .

Card 27. CON1, CON2, CON3, CON4, CONS, TO, HT, and HF. The thermal

conduc t iv i t i e s (Btu/hr*ft*OF) of t he ma te r i a l s i n each of the f i v e regions

should be entered i n the f i r s t f i v e da t a f i e l d s .

i n s ide sur face o f the r eac to r room wall, TO i n OR, t he he ight o f t he

r e a c t o r room, HT i n f t , and the f i lm coe f f i c i en t on the s i d e s of the a i r

channel, HF i n B t u / h t * f e o o F , should be entered i n da t a f i e l d s s i x through

e igh t .

26 cards (8F9.0).

The temperature on the

The format f o r t h i s card i s the same as t h a t f o r the previous

Card 28, TA, EPSIL, VEL, ACHAN, CP, RHO, and SIGMA a r e r e spec t ive ly 0 t he i n l e t a i r temperature,

channel (dimensionless and assumed t o be equal f o r both s i d e s o f t he a i r

channel), t he ve loc i ty of the air , f t / sec , the width o f the a i r channel,

ft?, t he s p e c i f i c hea t of air , Btu/lb-OF, the dens i ty of air, lb/ft?, and

the Stefan-Boltzmann constant (Btu/hr-ft? *OP),

entered according t o format 6F9.0, F18.0.

can be used f o r i d e n t i f i c a t i o n .

R, the emiss iv i ty of t he sur face o f t he a i r

These values must be

Again, the l a s t e igh t spaces

Preparat ion o f Case Data

Once the input d a t a have been supplied, one card must be prepared

f o r each case to be run.

and T6. EL1 through EL5 t o the material thicknesses ( f t ) t o

be used f o r each of the f

t u r e of t he ex te rna l sur f

The format 8F9.0 allows n

spaces f o r i d e n t i f i c a t i o n cases, the cards could be numbered

29 through 44. Numbering

quired. The firstSDO loo

5000 I = l , N where N is the number o f cases t o be run.

have the same a i r temperature, TA, and the statement immediately

This card conta ins EL1, EL2, EL3, EL4, EL5,

s i n the w a l l , and T6 i s the tempera-

concrete b io log ica l sh i e ld i n OR.

f o r each da ta f i e l d and the last e i g h t

the u s e r ' s convenience and i s not re- rogram must always be changed t o DO

A l l cases must w 1

-

52

following DO 5000 I = 1 , N must be w r i t t e n to correspond to the a i r temperature used.

ELS(I), T6(I), BOP(I), and BAM(1) must be checked t o see t h a t a s u f f i c i e n t

dimension size i s given t o allow a l l o f t he cases t o be run.

BAM(1) are dummy va r i ab le s and may be l e f t blank.

The DIMENSION statement containing ELl(1) through

BOP(1) and

Typical Computer Sheets

The assembly o f t he con t ro l cards, deck, input data , and case da ta

Typical cards f o r the TSS computer program i s i l l u s t r a t e d i n Fig. D. l .

d a t a f o r 32 cases to be run with one energy group a r e given i n Table D.1.

The output da t a at t h e bottom o f t h e a i r channel f o r one case are given

i n Table D.2, and the output da t a a t the top o f t he a i r channel f o r the

case are given i n Table D.3.

53 t

ks L

c

I

F i g . D . l . Assembly of Data Cards for TSS Computer Program.

54

55

1

56

3002 UP1 3003 V i ? !

57 n

hd I

I J'

I N A T l d Y THICUNFSSES (FEET)

.-.- -. _. . . . . . . . .- . . . . - . . - . . . . . - .

60

Appendix E

NOMENCLATURE

A = dimensionless constant used i n the Taylor buildup equation

4 = u n i t a rea of reactor room wall, f ta

C = s p e c i f i c hea t a t constant pressure, Btu/lb*'F P E = energy of inc ident gamma curren t , MeV

H = v e r t i c a l length o f a i r channel, f t

h = convective hea t t r a n s f e r coe f f i c i en t , Btu/hr*ft? *OF

k = thermal conductivity, Btu/hr*ft*'F '

- = equivalent conduct ivi ty where the subsc r ip t s a and b r e f e r t o ka-b

any two adjacent materials L 5: thickness o f a material lamination

Lch = width of a i r channel (dis tance between adjacent surfaces of

MWL = heat conduction rate out of the reactor room to the a i r channel,

f i r s t and second s t e e l gamma sh ie lds) , f t

Mw Q = volumetric gamma hea t ing rate, Btu/hr-f$

q* = hea t conduction rate out of the reactor room t t h e a i r channel,

Btu/hr= ft?

q i = rate a t which the gamma hea t generated i n the concrete is con-

ducted back toward the a i r channel, Btu /hr*f t?

Btu/hr* f t? T = temperature, OF

= rate of r ad ian t heat t r a n s f e r between the w a l l s of t h e a i r channel, QR

Ua = bulk ve loc i ty o f coolant air, f t / s e c

x = dis tance perpendicular to the sur face o f the r eac to r room w a l l , f t

a and ~3 = dimensionless cons tan ts used i n the Taylor builkup equation

E = sur face emiss iv i ty of walls o f a i r channel

0 = t i m e , hours

p = t o t a l gamma a t tenuat ion coe f f i c i en t , f t-1

% = gamma energy a t tenuat ion coe f f i c i en t , f t - l - <

w

61

p = density, lb/ft?

(J = Stefan-Boltzmann constant go = incident gamma current, photons/c# ‘sec

Subscripts Used With Terms

0 through 6 = numbers denoting a lamination interface as illustrated

in Fig. 2 and usually associated with temperature, T a = air c = concrete I = insulation i = energy group j = lamination s = skin lamination on reactor side of wall

FS = first steel gamma shield SS = second steel gamma field T = total

-C

U

63

ORNL TM-2029

Internal Distribution

1. M. Bender 2. C, E. Bettis 3. E. S. Bettis 4. E. G. Bohlmann 5. R. B. Briggs

6-7. W. K. Crowley 8. F. L. Culler 9. S. J. Ditto

10. H. G. Duggan 11. D. A. Dyslin 12. D. E. Ferguson 13. W. F. Ferguson 14. F. C. Fitzpatrick

15. C. l-l. Gabbard 16. W. R. Gall 17. W. R. Grimes

18. A. G. Grindell 19. 'P. N. Haubenreich

20. H. W. Hoffman , 21. P. R. Kasten

22. R. J. Kedl 23. G. H. Llewellyn 24. R. E. MacPherson 25. H. E. McCoy

26. R. L. Moore 27. H. A. Nelms

28. E. L. Nicholson 29. L. C. Oakes 30. A. M. Perry 31. T. W. Pickel

32-33. 34-35.

36. 37.

38. 39. 40. 41. 42. 43.

J. R. Rose M. W. Rosenthal Dunlap Scott W. C. Stoddart

D. A. Sunberg R. E. Thoma H. K. Walker J. R. Weir M. E. Whatley

J. C. White 44. W. R. Winsbro

45-46. Central Research Library

47. Document Reference Section 48. GE Division Library

49-58. Laboratory Records Department 59. Laboratory Records, ORNL R. C. 60. ORNL Patent Office

External Distribution

61. P. F. Pasqua, Nuclear Engineering Department, University of &ii Tennessee, Knoxville, Tennessee

62. L. R. Shobe, Engineering Mechanics Department, University of Tennessee, Knoxville, Tennessee '

63-77. Division of Technical Information Extension 78. Laboratory and University Division, USAEC, OR0

.